Sliding Mode Control For Stochastic Nonlinear Markovian Jump Systems

Sliding mode control(hereinafter referred to as SMC)is an effective control method for various types of system.Because of its robustness to system disturbance,it has applications in many areas on a large scale.In this article,we consider the SMC for two classes of stochastic Markovian jump systems(hereinafter referred to as MJSs)with nonlinear function.The summarization for the main conclusions of this paper is as follows:1.Observer-based SMC for stochastic nonlinear MJSsThe sliding mode control of a class of stochastic nonlinear markov jump systems is discussed.The system under consideration is affected by modal uncertainty,un-known nonlinear function,time-varying delay and external disturbance.These factors make the system more complex and more general.In addition,the transition proba-bility is partly unknown,which increases the difficulty of processing.The main task of this part is to design a sliding mode controller for this complex system,and it is based on observer.An observer is constructed first and an error system model is ob-tained.Then a new controller is designed to make integral sliding surface satisfies the reachable conditions.Under the sliding mode control law,Lyapunov functional is constructed,and a set of LMIs ensuring the stochastic stability of the closed-loop sys-tem is finally obtained by processing the matrix inequality and the partially unknown transition probability.Finally,a numerical example confirms the results of this study.2.Non-fragile SMC for stochastic nonlinear MJSs with actuator degradationWe study the sliding mode control for a class of stochastic nonlinear MJSs with system uncertainty and actuator failure.In this part,we design a new sliding mode controller,compared with the existing research,the controller at the same time con-sidering the actuator failure and controller gain perturbations,by considering a more general actuator failure model and the additional uncertainty is taken into accoun-t in the controller gain of perturbation matrix,effectively weakening the influence of actuator failures,make the model stability and the controller has more practical signif-icance.First,an appropriate integral sliding mode function is designed and a sliding mode controller is constructed.Then,on the premise of ensuring the accessibility of the sliding mode surface,Lyapunov function is constructed and the sliding mode con-trol law is synthesized.Finally,a set of strict sufficient conditions are given to ensure the stochastic stability of the system.A numerical example confirm the results of this study.